CK-12 Geometry-Concepts

http://www.ck12.org Chapter 4. Triangles and Congruence

Example A

What additional piece of information would you need to prove that these two triangles are congruent using the SAS
Postulate?

a)^6 ABC∼=^6 LKM

b)AB∼=LK

c)BC∼=KM

d)^6 BAC∼=^6 KLM

For the SAS Postulate, you need two sides and the included angle in both triangles. So, you need the side on the
other side of the angle. In 4 ABC, that isBCand in 4 LKMthat isKM. The correct answer is c.

Example B

Write a two-column proof to show that the two triangles are congruent.

Given:Cis the midpoint ofAEandDB

Prove: 4 ACB∼= 4 ECD

TABLE4.7:

Statement Reason

1.Cis the midpoint ofAEandDB Given

2.AC∼=CE,BC∼=CD Definition of a midpoint

3.^6 ACB∼=^6 DCE Vertical Angles Postulate
4. 4 ACB∼= 4 ECD SAS Postulate